Question

Write a recursive rule for the sequence -10,-3,4,11

Answer 1

Let the given sequence is -10,-3,4,11

The objective is to write recursive rule for the sequence.

In the given sequence each number has an equal difference between them

`\begin{gathered} -3-(-10)=7 \\ 4-(-3)=7 \\ 11-4=7 \end{gathered}`

So, consider the terms as,

`\begin{gathered} a_1=-10 \\ a_2=-3 \\ a_2=a_1+7 \\ a_3=a_2+7 \\ a_4=a_3+7 \end{gathered}`

Hence the recursive series is

`a_n=a_(n-1)+d`